Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
3293 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 3293 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#87521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#87518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11714179 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 4 | C2×#73027 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#73030 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#3025⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#33555 | — | 3 | 1 | no | maximal, Sylow |
| 8 | C2×#5950 | C22 | 1 | 1 | yes | characteristic |
| 9 | #87521 | C22 | 1 | 4 | yes | complemented |
| 10 | #87518 | C22 | 1 | 4 | yes | complemented |
| 11 | C2×#5934 | C22 | 1 | 2 | yes | — |
| 12 | C2×#5933 | C22 | 1 | 2 | yes | — |
| 13 | C2×#5912 | — | 4 | 1 | no | maximal |
| 14 | #3025⋊C3 | C22 | 1 | 4 | yes | complemented |
| 15 | C2×#458⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×B(4,𝔽2)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 17 | #73030 | C22 | 1 | 8 | yes | complemented |
| 18 | #73027 | C22 | 1 | 8 | yes | complemented |
| 19 | C2×#3540 | — | 3 | 1 | no | — |
| 20 | C2×#3027 | — | 3 | 1 | no | — |
| 21 | C2×#3025 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×#3022 | — | 3 | 1 | no | — |
| 23 | #33555 | — | 3 | 8 | no | — |
| 24 | #33555 | — | 3 | 8 | no | — |
| 25 | C2×#2199 | — | 3 | 2 | no | — |
| 26 | C2×#2199 | — | 3 | 2 | no | — |
| 27 | C2×#2197 | — | 3 | 2 | no | — |
| 28 | C2×#2197 | — | 3 | 2 | no | — |
| 29 | C2×#2129 | — | 3 | 1 | no | — |
| 30 | C2×#2122 | — | 3 | 1 | no | — |
| 31 | C2×#2120 | — | 3 | 1 | no | — |
| 32 | #5950 | C23 | 1 | 2 | yes | — |
| 33 | C2×#997 | C23 | 1 | 1 | yes | characteristic |
| 34 | C22×C4×A4 | — | 4 | 1 | no | — |
| 35 | #5934 | C23 | 1 | 4 | yes | — |
| 36 | #5933 | C23 | 1 | 4 | yes | — |
| 37 | C2×GL(2,ℤ/4) | — | 4 | 2 | no | — |
| 38 | C2×#984 | — | 8 | 1 | no | — |
| 39 | #5912 | — | 4 | 8 | no | — |
| 40 | C2×C4⋊S4 | — | 4 | 1 | no | — |
| 41 | C2×C4⋊S4 | — | 8 | 1 | no | — |
| 42 | C2×C4×S4 | — | 4 | 2 | no | — |
| 43 | C2×A4⋊Q8 | — | 4 | 1 | no | — |
| 44 | #458⋊C3 | C23 | 1 | 2 | yes | — |
| 45 | B(4,𝔽2)⋊C3 | C23 | 1 | 2 | yes | — |
| 46 | C2×#585 | C2×D3 | 1 | 1 | yes | characteristic |
| 47 | C22×#137 | — | 6 | 1 | no | — |
| 48 | #3540 | — | 3 | 8 | no | — |
| 49 | #3540 | — | 6 | 4 | no | — |
| 50 | #3540 | — | 6 | 4 | no | — |
| 51 | #3540 | — | 6 | 4 | no | — |
| 52 | C2×H(3,𝔽4) | — | 3 | 2 | no | — |
| 53 | C2×#560 | — | 6 | 1 | no | — |
| 54 | C2×#559 | — | 6 | 1 | no | — |
| 55 | C2×#556 | — | 6 | 1 | no | — |
| 56 | C2×#555 | — | 6 | 1 | no | — |
| 57 | C2×#551 | — | 3 | 2 | no | — |
| 58 | C2×#548 | — | 6 | 1 | no | — |
| 59 | C2×#546 | — | 6 | 1 | no | — |
| 60 | C2×#542 | — | 6 | 1 | no | — |
| 61 | C2×#542 | — | 6 | 2 | no | — |
| 62 | C2×#538 | — | 6 | 2 | no | — |
| 63 | C2×#536 | — | 3 | 1 | no | — |
| 64 | C2×#535 | — | 3 | 1 | no | — |
| 65 | C2×#535 | — | 6 | 1 | no | — |
| 66 | C2×#525 | — | 3 | 1 | no | — |
| 67 | C2×#525 | — | 6 | 1 | no | — |
| 68 | #3027 | — | 3 | 4 | no | — |
| 69 | #3027 | — | 3 | 4 | no | — |
| 70 | #3027 | — | 6 | 4 | no | — |
| 71 | #3025 | — | 3 | 4 | no | — |
| 72 | #3025 | C2×D3 | 1 | 4 | yes | complemented |
| 73 | C2×#458 | — | 3 | 1 | no | — |
| 74 | C2×#458 | C2×D3 | 1 | 1 | yes | characteristic |
| 75 | C2×B(4,𝔽2) | — | 3 | 1 | no | — |
| 76 | C2×B(4,𝔽2) | — | 3 | 2 | no | — |
| 77 | C2×B(4,𝔽2) | — | 3 | 2 | no | — |
| 78 | C2×B(4,𝔽2) | — | 6 | 2 | no | — |
| 79 | C2×B(4,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | #3022 | — | 3 | 4 | no | — |
| 81 | #3022 | — | 3 | 4 | no | — |
| 82 | #3022 | — | 6 | 4 | no | — |
| 83 | C2×#456 | — | 6 | 2 | no | — |
| 84 | C2×#455 | — | 3 | 2 | no | — |
| 85 | C2×#455 | — | 3 | 2 | no | — |
| 86 | C2×#421 | — | 6 | 1 | no | — |
| 87 | C2×#413 | — | 3 | 1 | no | — |
| 88 | C2×#410 | — | 3 | 1 | no | — |
| 89 | C2×#410 | — | 3 | 1 | no | — |
| 90 | C2×#410 | — | 6 | 1 | no | — |
| 91 | #2199 | — | 3 | 16 | no | — |
| 92 | #2199 | — | 3 | 8 | no | — |
| 93 | #2199 | — | 3 | 8 | no | — |
| 94 | #2197 | — | 3 | 16 | no | — |
| 95 | #2197 | — | 3 | 8 | no | — |
| 96 | #2197 | — | 3 | 8 | no | — |
| 97 | #2129 | — | 3 | 8 | no | — |
| 98 | C2×#354 | — | 3 | 2 | no | — |
| 99 | C2×#354 | — | 3 | 2 | no | — |
| 100 | #2122 | — | 3 | 8 | no | — |
| 101 | #2120 | — | 3 | 8 | no | — |
| 102 | C2×#352 | — | 3 | 2 | no | — |
| 103 | C2×AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 104 | C2×AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 105 | C2×AΣL(1,𝔽16) | — | 3 | 2 | no | — |
| 106 | C23×A4 | — | 4 | 1 | no | — |
| 107 | C22×S4 | — | 4 | 2 | no | — |
| 108 | C22×S4 | — | 8 | 2 | no | — |
| 109 | C2×#235 | — | 16 | 1 | no | — |
| 110 | #997 | C24 | 1 | 1 | yes | characteristic |
| 111 | C2×#41⋊C3 | — | 8 | 1 | no | — |
| 112 | C2×C4×A4 | — | 4 | 1 | no | — |
| 113 | C2×C4×A4 | — | 4 | 1 | no | — |
| 114 | C2×C4×A4 | — | 4 | 4 | no | — |
| 115 | C2×C4×A4 | — | 8 | 1 | no | — |
| 116 | GL(2,ℤ/4) | — | 4 | 8 | no | — |
| 117 | C2×SL(2,ℤ/4) | — | 4 | 2 | no | — |
| 118 | #984 | — | 8 | 4 | no | — |
| 119 | C2×#226 | — | 8 | 2 | no | — |
| 120 | C4⋊S4 | — | 4 | 4 | no | — |
| 121 | C4⋊S4 | — | 8 | 4 | no | — |
| 122 | C4×S4 | — | 4 | 8 | no | — |
| 123 | A4⋊Q8 | — | 4 | 4 | no | — |
| 124 | #585 | — | 3 | 2 | no | — |
| 125 | #585 | — | 6 | 2 | no | — |
| 126 | #585 | — | 6 | 2 | no | — |
| 127 | #585 | C22×D3 | 1 | 2 | yes | — |
| 128 | C2×2−1+4 | — | 6 | 1 | no | — |
| 129 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 130 | C2×H(5,𝔽2) | — | 6 | 1 | no | — |
| 131 | C2×H(5,𝔽2) | C22×D3 | 1 | 1 | yes | characteristic |
| 132 | C22×#41 | — | 3 | 1 | no | — |
| 133 | C22×#41 | — | 6 | 1 | no | — |
| 134 | C22×#41 | — | 6 | 1 | no | — |
| 135 | C22×#41 | — | 6 | 1 | no | — |
| 136 | C23×Q8 | — | 3 | 1 | no | — |
| 137 | C23×D4 | — | 3 | 1 | no | — |
| 138 | C24×C4 | S4 | 1 | 1 | yes | characteristic, complemented |
| 139 | C2×#137 | — | 6 | 2 | no | — |
| 140 | C2×#137 | — | 6 | 2 | no | — |
| 141 | C2×#137 | — | 6 | 4 | no | — |
| 142 | C2×#137 | — | 6 | 4 | no | — |
| 143 | C2×#137 | — | 12 | 1 | no | — |
| 144 | C2×#137 | — | 12 | 2 | no | — |
| 145 | C2×#137 | — | 12 | 1 | no | — |
| 146 | C2×#137 | — | 12 | 2 | no | — |
| 147 | C22×Q16 | — | 12 | 1 | no | — |
| 148 | C22×SD16 | — | 12 | 1 | no | — |
| 149 | C22×M16 | — | 6 | 1 | no | — |
| 150 | H(3,𝔽4) | — | 3 | 8 | no | — |
| 151 | H(3,𝔽4) | — | 6 | 4 | no | — |
| 152 | H(3,𝔽4) | — | 6 | 4 | no | — |
| 153 | H(3,𝔽4) | — | 6 | 4 | no | — |
| 154 | #560 | — | 6 | 8 | no | — |
| 155 | #560 | — | 6 | 8 | no | — |
| 156 | #559 | — | 6 | 8 | no | — |
| 157 | #559 | — | 6 | 8 | no | — |
| 158 | #556 | — | 6 | 8 | no | — |
| 159 | #556 | — | 6 | 8 | no | — |
| 160 | #555 | — | 6 | 8 | no | — |
| 161 | #555 | — | 6 | 8 | no | — |
| 162 | #551 | — | 3 | 8 | no | — |
| 163 | #551 | — | 6 | 4 | no | — |
| 164 | #551 | — | 6 | 4 | no | — |
| 165 | #551 | — | 6 | 4 | no | — |
| 166 | #548 | — | 6 | 8 | no | — |
| 167 | #548 | — | 6 | 8 | no | — |
| 168 | #546 | — | 6 | 8 | no | — |
| 169 | #546 | — | 6 | 8 | no | — |
| 170 | #542 | — | 6 | 8 | no | — |
| 171 | #542 | — | 6 | 16 | no | — |
| 172 | #542 | — | 6 | 8 | no | — |
| 173 | #542 | — | 6 | 16 | no | — |
| 174 | #538 | — | 6 | 16 | no | — |
| 175 | #538 | — | 6 | 16 | no | — |
| 176 | #536 | — | 3 | 4 | no | — |
| 177 | #536 | — | 3 | 4 | no | — |
| 178 | #536 | — | 6 | 2 | no | — |
| 179 | #536 | — | 6 | 2 | no | — |
| 180 | #535 | — | 3 | 4 | no | — |
| 181 | #535 | — | 3 | 4 | no | — |
| 182 | #535 | — | 6 | 2 | no | — |
| 183 | #535 | — | 6 | 2 | no | — |
| 184 | #535 | — | 6 | 4 | no | — |
| 185 | #535 | — | 6 | 4 | no | — |
| 186 | #535 | — | 12 | 2 | no | — |
| 187 | #535 | — | 12 | 2 | no | — |
| 188 | C2×C4⋊Q8 | — | 3 | 2 | no | — |
| 189 | C2×C4⋊Q8 | — | 6 | 1 | no | — |
| 190 | C2×#127 | — | 6 | 1 | no | — |
| 191 | C2×#127 | — | 12 | 1 | no | — |
| 192 | C2×#126 | — | 6 | 2 | no | — |
| 193 | C2×#126 | — | 6 | 2 | no | — |
| 194 | C2×#126 | — | 6 | 2 | no | — |
| 195 | C2×#124 | — | 3 | 2 | no | — |
| 196 | C2×#124 | — | 6 | 2 | no | — |
| 197 | C2×#124 | — | 6 | 2 | no | — |
| 198 | C2×#124 | — | 6 | 2 | no | — |
| 199 | C2×#124 | — | 6 | 1 | no | — |
| 200 | C2×#124 | — | 6 | 2 | no | — |
| 201 | C2×#124 | — | 6 | 2 | no | — |
| 202 | C2×#124 | — | 6 | 1 | no | — |
| 203 | C2×#124 | — | 12 | 1 | no | — |
| 204 | #525 | — | 3 | 4 | no | — |
| 205 | #525 | — | 3 | 4 | no | — |
| 206 | #525 | — | 6 | 2 | no | — |
| 207 | #525 | — | 6 | 2 | no | — |
| 208 | #525 | — | 6 | 8 | no | — |
| 209 | #525 | — | 6 | 8 | no | — |
| 210 | C2×#123 | — | 3 | 1 | no | — |
| 211 | C2×#123 | — | 3 | 1 | no | — |
| 212 | C2×#123 | — | 6 | 2 | no | — |
| 213 | C2×#123 | — | 6 | 1 | no | — |
| 214 | C2×#123 | — | 6 | 1 | no | — |
| 215 | C2×#123 | — | 6 | 2 | no | — |
| 216 | C2×#123 | — | 6 | 2 | no | — |
| 217 | C2×C22⋊Q8 | — | 6 | 1 | no | — |
| 218 | C2×C22⋊Q8 | — | 6 | 1 | no | — |
| 219 | C2×C22⋊Q8 | — | 6 | 2 | no | — |
| 220 | C2×C22⋊Q8 | — | 6 | 1 | no | — |
| 221 | C2×C22⋊Q8 | — | 6 | 2 | no | — |
| 222 | C2×C22⋊Q8 | — | 6 | 1 | no | — |
| 223 | C2×#121 | — | 6 | 1 | no | — |
| 224 | C2×#121 | — | 6 | 1 | no | — |
| 225 | C2×#121 | — | 6 | 1 | no | — |
| 226 | C2×#121 | — | 6 | 2 | no | — |
| 227 | C2×#121 | — | 6 | 2 | no | — |
| 228 | C2×#121 | — | 6 | 2 | no | — |
| 229 | C2×#121 | — | 6 | 1 | no | — |
| 230 | C2×#121 | — | 12 | 1 | no | — |
| 231 | C2×#121 | — | 12 | 1 | no | — |
| 232 | C2×#120 | — | 3 | 2 | no | — |
| 233 | C2×#120 | — | 3 | 2 | no | — |
| 234 | C2×#120 | — | 3 | 1 | no | — |
| 235 | C2×#120 | — | 3 | 1 | no | — |
| 236 | C2×#120 | — | 6 | 2 | no | — |
| 237 | C2×#120 | — | 6 | 2 | no | — |
| 238 | C2×#120 | — | 6 | 2 | no | — |
| 239 | C2×#120 | — | 6 | 2 | no | — |
| 240 | C2×C4×Q8 | — | 6 | 1 | no | — |
| 241 | C2×C4×Q8 | — | 6 | 2 | no | — |
| 242 | C2×C4×D4 | — | 6 | 1 | no | — |
| 243 | C2×C4×D4 | — | 6 | 1 | no | — |
| 244 | C2×C4×D4 | — | 6 | 2 | no | — |
| 245 | C2×C4×D4 | — | 6 | 2 | no | — |
| 246 | C2×C4×D4 | — | 6 | 1 | no | — |
| 247 | C2×C4×D4 | — | 6 | 2 | no | — |
| 248 | C2×#117 | — | 3 | 1 | no | — |
| 249 | C2×#117 | — | 3 | 1 | no | — |
| 250 | C2×#117 | — | 3 | 1 | no | — |
| 251 | C2×#117 | — | 6 | 2 | no | — |
| 252 | C2×#117 | — | 6 | 1 | no | — |
| 253 | C2×#117 | — | 6 | 1 | no | — |
| 254 | C22×C22⋊C4 | — | 6 | 2 | no | — |
| 255 | #458 | — | 3 | 4 | no | — |
| 256 | #458 | — | 3 | 2 | no | — |
| 257 | #458 | — | 6 | 2 | no | — |
| 258 | #458 | C22×D3 | 1 | 2 | yes | — |
| 259 | B(4,𝔽2) | — | 3 | 4 | no | — |
| 260 | B(4,𝔽2) | — | 3 | 2 | no | — |
| 261 | B(4,𝔽2) | — | 3 | 8 | no | — |
| 262 | B(4,𝔽2) | — | 3 | 4 | no | — |
| 263 | B(4,𝔽2) | — | 3 | 4 | no | — |
| 264 | B(4,𝔽2) | — | 6 | 2 | no | — |
| 265 | B(4,𝔽2) | — | 6 | 4 | no | — |
| 266 | B(4,𝔽2) | — | 6 | 4 | no | — |
| 267 | B(4,𝔽2) | — | 6 | 8 | no | — |
| 268 | B(4,𝔽2) | — | 6 | 8 | no | — |
| 269 | B(4,𝔽2) | C22×D3 | 1 | 2 | yes | — |
| 270 | #456 | — | 6 | 8 | no | — |
| 271 | #456 | — | 6 | 8 | no | — |
| 272 | #455 | — | 3 | 8 | no | — |
| 273 | #455 | — | 3 | 4 | no | — |
| 274 | #455 | — | 3 | 4 | no | — |
| 275 | #455 | — | 6 | 4 | no | — |
| 276 | #455 | — | 6 | 4 | no | — |
| 277 | #421 | — | 6 | 4 | no | — |
| 278 | #421 | — | 6 | 4 | no | — |
| 279 | C2×#104 | — | 6 | 2 | no | — |
| 280 | C2×#104 | — | 6 | 2 | no | — |
| 281 | #413 | — | 3 | 4 | no | — |
| 282 | #413 | — | 6 | 2 | no | — |
| 283 | C2×#101 | — | 6 | 1 | no | — |
| 284 | C2×#100 | — | 3 | 2 | no | — |
| 285 | #410 | — | 3 | 4 | no | — |
| 286 | #410 | — | 3 | 4 | no | — |
| 287 | #410 | — | 6 | 2 | no | — |
| 288 | #410 | — | 6 | 4 | no | — |
| 289 | #410 | — | 6 | 4 | no | — |
| 290 | #410 | — | 6 | 2 | no | — |
| 291 | C2×#99 | — | 3 | 1 | no | — |
| 292 | C2×#99 | — | 3 | 1 | no | — |
| 293 | C2×#99 | — | 3 | 2 | no | — |
| 294 | C2×#99 | — | 6 | 1 | no | — |
| 295 | C2×#99 | — | 6 | 2 | no | — |
| 296 | C2×#99 | — | 6 | 2 | no | — |
| 297 | C2×#99 | — | 6 | 1 | no | — |
| 298 | #354 | — | 3 | 8 | no | — |
| 299 | #354 | — | 3 | 8 | no | — |
| 300 | #352 | — | 3 | 8 | no | — |
| 301 | AΣL(1,𝔽16) | — | 3 | 8 | no | — |
| 302 | AΣL(1,𝔽16) | — | 3 | 8 | no | — |
| 303 | AΣL(1,𝔽16) | — | 3 | 8 | no | — |
| 304 | C22×A4 | — | 4 | 1 | no | — |
| 305 | C22×A4 | — | 4 | 2 | no | — |
| 306 | C22×A4 | — | 8 | 1 | no | — |
| 307 | C22×A4 | — | 8 | 2 | no | — |
| 308 | C2×S4 | — | 4 | 4 | no | — |
| 309 | C2×S4 | — | 8 | 4 | no | — |
| 310 | C2×S4 | — | 8 | 4 | no | — |
| 311 | C2×S4 | — | 16 | 4 | no | — |
| 312 | C22×C3×C4 | — | 16 | 1 | no | — |
| 313 | C2×#67 | — | 16 | 2 | no | — |
| 314 | #235 | — | 16 | 8 | no | — |
| 315 | C2×D12 | — | 16 | 1 | no | — |
| 316 | C2×C4×D3 | — | 16 | 2 | no | — |
| 317 | C2×Dic6 | — | 16 | 1 | no | — |
| 318 | #41⋊C3 | — | 8 | 2 | no | — |
| 319 | C2×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 320 | C4×A4 | — | 4 | 2 | no | — |
| 321 | C4×A4 | — | 4 | 2 | no | — |
| 322 | C4×A4 | — | 8 | 2 | no | — |
| 323 | SL(2,ℤ/4) | — | 4 | 4 | no | — |
| 324 | #226 | — | 8 | 4 | no | — |
| 325 | C25 | — | 3 | 2 | no | — |
| 326 | C25 | C2×S4 | 1 | 1 | yes | characteristic |
| 327 | 2−1+4 | — | 6 | 2 | no | — |
| 328 | 2−1+4 | — | 6 | 2 | no | — |
| 329 | 2−1+4 | — | 12 | 2 | no | — |
| 330 | 2−1+4 | — | 12 | 2 | no | — |
| 331 | 2−1+4 | — | 12 | 1 | no | — |
| 332 | 2−1+4 | — | 12 | 1 | no | — |
| 333 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 334 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 335 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 336 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 337 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 338 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 339 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 340 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 341 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 342 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 343 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 344 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 345 | H(5,𝔽2) | — | 12 | 1 | no | — |
| 346 | H(5,𝔽2) | — | 12 | 1 | no | — |
| 347 | H(5,𝔽2) | C23×D3 | 1 | 1 | yes | characteristic |
| 348 | C2×#41 | — | 2 | 1 | no | — |
| 349 | C2×#41 | — | 3 | 2 | no | — |
| 350 | C2×#41 | — | 3 | 2 | no | — |
| 351 | C2×#41 | — | 3 | 2 | no | — |
| 352 | C2×#41 | — | 3 | 2 | no | — |
| 353 | C2×#41 | — | 6 | 2 | no | — |
| 354 | C2×#41 | — | 6 | 2 | no | — |
| 355 | C2×#41 | — | 6 | 2 | no | — |
| 356 | C2×#41 | — | 6 | 1 | no | — |
| 357 | C2×#41 | — | 6 | 2 | no | — |
| 358 | C2×#41 | — | 6 | 1 | no | — |
| 359 | C2×#41 | — | 6 | 2 | no | — |
| 360 | C2×#41 | — | 6 | 2 | no | — |
| 361 | C2×#41 | — | 6 | 8 | no | — |
| 362 | C2×#41 | — | 6 | 1 | no | — |
| 363 | C2×#41 | — | 6 | 2 | no | — |
| 364 | C2×#41 | — | 6 | 2 | no | — |
| 365 | C2×#41 | — | 12 | 1 | no | — |
| 366 | C2×#41 | — | 12 | 1 | no | — |
| 367 | C2×#41 | — | 12 | 2 | no | — |
| 368 | C2×#41 | — | 12 | 1 | no | — |
| 369 | C2×#41 | — | 12 | 2 | no | — |
| 370 | C2×#41 | — | 12 | 2 | no | — |
| 371 | C2×#41 | — | 12 | 1 | no | — |
| 372 | C2×#41 | — | 12 | 1 | no | — |
| 373 | C2×#41 | — | 12 | 2 | no | — |
| 374 | C2×#41 | — | 12 | 2 | no | — |
| 375 | C2×#41 | — | 24 | 1 | no | — |
| 376 | C2×#41 | — | 24 | 2 | no | — |
| 377 | C2×#41 | — | 24 | 1 | no | — |
| 378 | C22×Q8 | — | 3 | 1 | no | — |
| 379 | C22×Q8 | — | 3 | 2 | no | — |
| 380 | C22×Q8 | — | 3 | 4 | no | — |
| 381 | C22×Q8 | — | 6 | 1 | no | — |
| 382 | C22×Q8 | — | 6 | 2 | no | — |
| 383 | C22×Q8 | — | 6 | 1 | no | — |
| 384 | C22×Q8 | — | 6 | 2 | no | — |
| 385 | C22×Q8 | — | 6 | 1 | no | — |
| 386 | C22×Q8 | — | 12 | 1 | no | — |
| 387 | C22×Q8 | — | 12 | 2 | no | — |
| 388 | C22×Q8 | — | 12 | 1 | no | — |
| 389 | C22×D4 | — | 3 | 1 | no | — |
| 390 | C22×D4 | — | 3 | 1 | no | — |
| 391 | C22×D4 | — | 3 | 1 | no | — |
| 392 | C22×D4 | — | 3 | 4 | no | — |
| 393 | C22×D4 | — | 6 | 1 | no | — |
| 394 | C22×D4 | — | 6 | 1 | no | — |
| 395 | C22×D4 | — | 6 | 2 | no | — |
| 396 | C22×D4 | — | 6 | 1 | no | — |
| 397 | C22×D4 | — | 6 | 1 | no | — |
| 398 | C22×D4 | — | 6 | 1 | no | — |
| 399 | C22×D4 | — | 6 | 1 | no | — |
| 400 | C22×D4 | — | 6 | 1 | no | — |
| 401 | C22×D4 | — | 6 | 1 | no | — |
| 402 | C22×D4 | — | 6 | 2 | no | — |
| 403 | C22×D4 | — | 6 | 2 | no | — |
| 404 | C22×D4 | — | 6 | 2 | no | — |
| 405 | C22×D4 | — | 6 | 2 | no | — |
| 406 | C22×D4 | — | 12 | 1 | no | — |
| 407 | C22×D4 | — | 12 | 1 | no | — |
| 408 | C22×D4 | — | 12 | 2 | no | — |
| 409 | C22×D4 | — | 12 | 1 | no | — |
| 410 | C22×D4 | — | 12 | 2 | no | — |
| 411 | C22×D4 | — | 12 | 2 | no | — |
| 412 | C23×C4 | — | 2 | 1 | no | — |
| 413 | C23×C4 | — | 3 | 1 | no | — |
| 414 | C23×C4 | — | 3 | 1 | no | — |
| 415 | C23×C4 | — | 6 | 1 | no | — |
| 416 | C23×C4 | — | 6 | 1 | no | — |
| 417 | C23×C4 | — | 6 | 2 | no | — |
| 418 | C23×C4 | — | 6 | 1 | no | — |
| 419 | C23×C4 | — | 6 | 1 | no | — |
| 420 | C23×C4 | — | 6 | 2 | no | — |
| 421 | C23×C4 | — | 6 | 2 | no | — |
| 422 | C23×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 423 | C23×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 424 | C23×C4 | C2×S4 | 1 | 4 | yes | complemented |
| 425 | #137 | — | 6 | 4 | no | — |
| 426 | #137 | — | 6 | 4 | no | — |
| 427 | #137 | — | 6 | 8 | no | — |
| 428 | #137 | — | 12 | 4 | no | — |
| 429 | #137 | — | 12 | 2 | no | — |
| 430 | #137 | — | 12 | 2 | no | — |
| 431 | #137 | — | 12 | 4 | no | — |
| 432 | #137 | — | 12 | 4 | no | — |
| 433 | #137 | — | 12 | 4 | no | — |
| 434 | #137 | — | 12 | 4 | no | — |
| 435 | C2×Q16 | — | 12 | 2 | no | — |
| 436 | C2×Q16 | — | 12 | 4 | no | — |
| 437 | C2×Q16 | — | 12 | 2 | no | — |
| 438 | C2×Q16 | — | 12 | 4 | no | — |
| 439 | C2×SD16 | — | 12 | 2 | no | — |
| 440 | C2×SD16 | — | 12 | 2 | no | — |
| 441 | C2×SD16 | — | 12 | 4 | no | — |
| 442 | C2×SD16 | — | 12 | 4 | no | — |
| 443 | C2×M16 | — | 6 | 2 | no | — |
| 444 | C2×M16 | — | 6 | 4 | no | — |
| 445 | C2×M16 | — | 12 | 2 | no | — |
| 446 | C2×M16 | — | 12 | 1 | no | — |
| 447 | C22×C8 | — | 12 | 1 | no | — |
| 448 | C4⋊Q8 | — | 3 | 8 | no | — |
| 449 | C4⋊Q8 | — | 6 | 4 | no | — |
| 450 | C4⋊Q8 | — | 6 | 8 | no | — |
| 451 | #127 | — | 6 | 4 | no | — |
| 452 | #127 | — | 6 | 4 | no | — |
| 453 | #127 | — | 12 | 4 | no | — |
| 454 | #127 | — | 12 | 4 | no | — |
| 455 | #126 | — | 6 | 8 | no | — |
| 456 | #126 | — | 6 | 16 | no | — |
| 457 | #126 | — | 6 | 8 | no | — |
| 458 | #126 | — | 6 | 16 | no | — |
| 459 | #124 | — | 3 | 4 | no | — |
| 460 | #124 | — | 3 | 4 | no | — |
| 461 | #124 | — | 6 | 8 | no | — |
| 462 | #124 | — | 6 | 8 | no | — |
| 463 | #124 | — | 6 | 8 | no | — |
| 464 | #124 | — | 6 | 2 | no | — |
| 465 | #124 | — | 6 | 2 | no | — |
| 466 | #124 | — | 6 | 4 | no | — |
| 467 | #124 | — | 6 | 4 | no | — |
| 468 | #124 | — | 6 | 8 | no | — |
| 469 | #124 | — | 6 | 16 | no | — |
| 470 | #124 | — | 6 | 8 | no | — |
| 471 | #124 | — | 6 | 8 | no | — |
| 472 | #124 | — | 6 | 8 | no | — |
| 473 | #124 | — | 6 | 8 | no | — |
| 474 | #124 | — | 6 | 8 | no | — |
| 475 | #124 | — | 12 | 4 | no | — |
| 476 | #124 | — | 12 | 4 | no | — |
| 477 | #123 | — | 3 | 2 | no | — |
| 478 | #123 | — | 3 | 2 | no | — |
| 479 | #123 | — | 3 | 4 | no | — |
| 480 | #123 | — | 6 | 8 | no | — |
| 481 | #123 | — | 6 | 1 | no | — |
| 482 | #123 | — | 6 | 1 | no | — |
| 483 | #123 | — | 6 | 2 | no | — |
| 484 | #123 | — | 6 | 4 | no | — |
| 485 | #123 | — | 6 | 4 | no | — |
| 486 | #123 | — | 6 | 4 | no | — |
| 487 | #123 | — | 6 | 4 | no | — |
| 488 | #123 | — | 6 | 16 | no | — |
| 489 | #123 | — | 6 | 16 | no | — |
| 490 | #123 | — | 6 | 8 | no | — |
| 491 | C22⋊Q8 | — | 6 | 4 | no | — |
| 492 | C22⋊Q8 | — | 6 | 4 | no | — |
| 493 | C22⋊Q8 | — | 6 | 4 | no | — |
| 494 | C22⋊Q8 | — | 6 | 4 | no | — |
| 495 | C22⋊Q8 | — | 6 | 4 | no | — |
| 496 | C22⋊Q8 | — | 6 | 8 | no | — |
| 497 | C22⋊Q8 | — | 6 | 8 | no | — |
| 498 | C22⋊Q8 | — | 6 | 16 | no | — |
| 499 | C22⋊Q8 | — | 6 | 8 | no | — |
| 500 | C22⋊Q8 | — | 6 | 4 | no | — |
| 501 | #121 | — | 6 | 4 | no | — |
| 502 | #121 | — | 6 | 4 | no | — |
| 503 | #121 | — | 6 | 4 | no | — |
| 504 | #121 | — | 6 | 4 | no | — |
| 505 | #121 | — | 6 | 4 | no | — |
| 506 | #121 | — | 6 | 8 | no | — |
| 507 | #121 | — | 6 | 16 | no | — |
| 508 | #121 | — | 6 | 16 | no | — |
| 509 | #121 | — | 6 | 16 | no | — |
| 510 | #121 | — | 6 | 4 | no | — |
| 511 | #121 | — | 12 | 4 | no | — |
| 512 | #121 | — | 12 | 4 | no | — |
| 513 | #121 | — | 12 | 4 | no | — |
| 514 | #121 | — | 12 | 4 | no | — |
| 515 | #120 | — | 3 | 8 | no | — |
| 516 | #120 | — | 3 | 4 | no | — |
| 517 | #120 | — | 3 | 4 | no | — |
| 518 | #120 | — | 3 | 4 | no | — |
| 519 | #120 | — | 3 | 2 | no | — |
| 520 | #120 | — | 3 | 2 | no | — |
| 521 | #120 | — | 6 | 2 | no | — |
| 522 | #120 | — | 6 | 1 | no | — |
| 523 | #120 | — | 6 | 1 | no | — |
| 524 | #120 | — | 6 | 4 | no | — |
| 525 | #120 | — | 6 | 2 | no | — |
| 526 | #120 | — | 6 | 2 | no | — |
| 527 | #120 | — | 6 | 8 | no | — |
| 528 | #120 | — | 6 | 8 | no | — |
| 529 | #120 | — | 6 | 8 | no | — |
| 530 | #120 | — | 6 | 8 | no | — |
| 531 | #120 | — | 6 | 4 | no | — |
| 532 | #120 | — | 6 | 8 | no | — |
| 533 | #120 | — | 6 | 4 | no | — |
| 534 | #120 | — | 12 | 2 | no | — |
| 535 | #120 | — | 12 | 2 | no | — |
| 536 | #120 | — | 12 | 4 | no | — |
| 537 | C4×Q8 | — | 6 | 8 | no | — |
| 538 | C4×Q8 | — | 6 | 16 | no | — |
| 539 | C4×D4 | — | 6 | 4 | no | — |
| 540 | C4×D4 | — | 6 | 4 | no | — |
| 541 | C4×D4 | — | 6 | 4 | no | — |
| 542 | C4×D4 | — | 6 | 4 | no | — |
| 543 | C4×D4 | — | 6 | 16 | no | — |
| 544 | C4×D4 | — | 6 | 8 | no | — |
| 545 | C4×D4 | — | 6 | 16 | no | — |
| 546 | C4×D4 | — | 6 | 8 | no | — |
| 547 | C4×D4 | — | 6 | 8 | no | — |
| 548 | #117 | — | 3 | 4 | no | — |
| 549 | #117 | — | 3 | 4 | no | — |
| 550 | #117 | — | 3 | 4 | no | — |
| 551 | #117 | — | 6 | 8 | no | — |
| 552 | #117 | — | 6 | 2 | no | — |
| 553 | #117 | — | 6 | 2 | no | — |
| 554 | #117 | — | 6 | 2 | no | — |
| 555 | #117 | — | 6 | 8 | no | — |
| 556 | #117 | — | 6 | 8 | no | — |
| 557 | #117 | — | 6 | 4 | no | — |
| 558 | #117 | — | 12 | 2 | no | — |
| 559 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 560 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 561 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 562 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 563 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 564 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 565 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 566 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 567 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 568 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 569 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 570 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 571 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 572 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 573 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 574 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 575 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 576 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 577 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 578 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 579 | C2×C22⋊C4 | — | 6 | 8 | no | — |
| 580 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 581 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 582 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 583 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 584 | C2×C22⋊C4 | — | 6 | 8 | no | — |
| 585 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 586 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 587 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 588 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 589 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 590 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 591 | C2×C22⋊C4 | — | 12 | 2 | no | — |
| 592 | C2×C22⋊C4 | — | 12 | 2 | no | — |
| 593 | C2×C42 | — | 3 | 2 | no | — |
| 594 | C2×C42 | — | 6 | 1 | no | — |
| 595 | C2×C42 | — | 6 | 1 | no | — |
| 596 | C2×C42 | — | 6 | 2 | no | — |
| 597 | C2×C42 | — | 6 | 2 | no | — |
| 598 | C2×C42 | — | 12 | 1 | no | — |
| 599 | #104 | — | 6 | 4 | no | — |
| 600 | #104 | — | 6 | 8 | no | — |
| 601 | #104 | — | 6 | 4 | no | — |
| 602 | #101 | — | 6 | 4 | no | — |
| 603 | #100 | — | 3 | 4 | no | — |
| 604 | #100 | — | 6 | 2 | no | — |
| 605 | #99 | — | 3 | 2 | no | — |
| 606 | #99 | — | 3 | 2 | no | — |
| 607 | #99 | — | 3 | 4 | no | — |
| 608 | #99 | — | 6 | 1 | no | — |
| 609 | #99 | — | 6 | 1 | no | — |
| 610 | #99 | — | 6 | 4 | no | — |
| 611 | #99 | — | 6 | 4 | no | — |
| 612 | #99 | — | 6 | 8 | no | — |
| 613 | #99 | — | 6 | 4 | no | — |
| 614 | #99 | — | 6 | 2 | no | — |
| 615 | #99 | — | 6 | 4 | no | — |
| 616 | C23×C3 | — | 16 | 1 | no | — |
| 617 | C22×D3 | — | 16 | 2 | no | — |
| 618 | C2×A4 | — | 4 | 2 | no | — |
| 619 | C2×A4 | — | 4 | 1 | no | — |
| 620 | C2×A4 | — | 8 | 1 | no | — |
| 621 | C2×A4 | — | 8 | 2 | no | — |
| 622 | C2×A4 | — | 8 | 2 | no | — |
| 623 | S4 | — | 8 | 4 | no | — |
| 624 | S4 | — | 16 | 4 | no | — |
| 625 | C2×C3×C4 | — | 16 | 1 | no | — |
| 626 | C2×C3×C4 | — | 16 | 4 | no | — |
| 627 | C2×C3×C4 | — | 16 | 1 | no | — |
| 628 | #67 | — | 16 | 8 | no | — |
| 629 | C2×Dic3 | — | 16 | 2 | no | — |
| 630 | D12 | — | 16 | 4 | no | — |
| 631 | C4×D3 | — | 16 | 8 | no | — |
| 632 | Dic6 | — | 16 | 4 | no | — |
| 633 | SL(2,𝔽3) | — | 8 | 1 | no | — |
| 634 | C24 | — | 2 | 1 | no | — |
| 635 | C24 | — | 3 | 1 | no | — |
| 636 | C24 | — | 3 | 1 | no | — |
| 637 | C24 | — | 3 | 4 | no | — |
| 638 | C24 | — | 6 | 1 | no | — |
| 639 | C24 | — | 6 | 2 | no | — |
| 640 | C24 | — | 6 | 1 | no | — |
| 641 | C24 | — | 6 | 2 | no | — |
| 642 | C24 | — | 6 | 1 | no | — |
| 643 | C24 | — | 8 | 2 | no | — |
| 644 | C24 | — | 12 | 2 | no | — |
| 645 | C24 | — | 12 | 2 | no | — |
| 646 | C24 | — | 24 | 4 | no | — |
| 647 | C24 | C22×S4 | 1 | 1 | yes | characteristic |
| 648 | C24 | C22×S4 | 1 | 2 | yes | — |
| 649 | #41 | — | 2 | 2 | no | — |
| 650 | #41 | — | 6 | 1 | no | — |
| 651 | #41 | — | 6 | 2 | no | — |
| 652 | #41 | — | 6 | 1 | no | — |
| 653 | #41 | — | 6 | 2 | no | — |
| 654 | #41 | — | 6 | 2 | no | — |
| 655 | #41 | — | 6 | 2 | no | — |
| 656 | #41 | — | 6 | 1 | no | — |
| 657 | #41 | — | 6 | 1 | no | — |
| 658 | #41 | — | 6 | 2 | no | — |
| 659 | #41 | — | 12 | 2 | no | — |
| 660 | #41 | — | 12 | 2 | no | — |
| 661 | #41 | — | 12 | 2 | no | — |
| 662 | #41 | — | 12 | 2 | no | — |
| 663 | #41 | — | 12 | 2 | no | — |
| 664 | #41 | — | 12 | 2 | no | — |
| 665 | #41 | — | 12 | 1 | no | — |
| 666 | #41 | — | 12 | 2 | no | — |
| 667 | #41 | — | 12 | 1 | no | — |
| 668 | #41 | — | 12 | 2 | no | — |
| 669 | #41 | — | 12 | 2 | no | — |
| 670 | #41 | — | 12 | 2 | no | — |
| 671 | #41 | — | 12 | 2 | no | — |
| 672 | #41 | — | 12 | 2 | no | — |
| 673 | #41 | — | 12 | 2 | no | — |
| 674 | #41 | — | 12 | 1 | no | — |
| 675 | #41 | — | 12 | 2 | no | — |
| 676 | #41 | — | 12 | 2 | no | — |
| 677 | #41 | — | 12 | 2 | no | — |
| 678 | #41 | — | 12 | 2 | no | — |
| 679 | #41 | — | 12 | 2 | no | — |
| 680 | #41 | — | 12 | 2 | no | — |
| 681 | #41 | — | 12 | 2 | no | — |
| 682 | #41 | — | 12 | 2 | no | — |
| 683 | #41 | — | 12 | 1 | no | — |
| 684 | #41 | — | 24 | 8 | no | — |
| 685 | #41 | — | 24 | 8 | no | — |
| 686 | C2×Q8 | — | 2 | 1 | no | — |
| 687 | C2×Q8 | — | 3 | 2 | no | — |
| 688 | C2×Q8 | — | 3 | 2 | no | — |
| 689 | C2×Q8 | — | 3 | 4 | no | — |
| 690 | C2×Q8 | — | 6 | 4 | no | — |
| 691 | C2×Q8 | — | 6 | 2 | no | — |
| 692 | C2×Q8 | — | 6 | 2 | no | — |
| 693 | C2×Q8 | — | 6 | 2 | no | — |
| 694 | C2×Q8 | — | 6 | 8 | no | — |
| 695 | C2×Q8 | — | 6 | 1 | no | — |
| 696 | C2×Q8 | — | 6 | 2 | no | — |
| 697 | C2×Q8 | — | 6 | 2 | no | — |
| 698 | C2×Q8 | — | 12 | 1 | no | — |
| 699 | C2×Q8 | — | 12 | 1 | no | — |
| 700 | C2×Q8 | — | 12 | 2 | no | — |
| 701 | C2×Q8 | — | 12 | 1 | no | — |
| 702 | C2×Q8 | — | 12 | 2 | no | — |
| 703 | C2×Q8 | — | 12 | 2 | no | — |
| 704 | C2×Q8 | — | 12 | 2 | no | — |
| 705 | C2×Q8 | — | 12 | 2 | no | — |
| 706 | C2×Q8 | — | 12 | 4 | no | — |
| 707 | C2×Q8 | — | 12 | 4 | no | — |
| 708 | C2×Q8 | — | 12 | 1 | no | — |
| 709 | C2×Q8 | — | 24 | 2 | no | — |
| 710 | C2×Q8 | — | 24 | 2 | no | — |
| 711 | C2×Q8 | — | 24 | 4 | no | — |
| 712 | C2×D4 | — | 3 | 1 | no | — |
| 713 | C2×D4 | — | 3 | 2 | no | — |
| 714 | C2×D4 | — | 3 | 1 | no | — |
| 715 | C2×D4 | — | 3 | 2 | no | — |
| 716 | C2×D4 | — | 3 | 2 | no | — |
| 717 | C2×D4 | — | 3 | 1 | no | — |
| 718 | C2×D4 | — | 3 | 1 | no | — |
| 719 | C2×D4 | — | 3 | 2 | no | — |
| 720 | C2×D4 | — | 6 | 4 | no | — |
| 721 | C2×D4 | — | 6 | 4 | no | — |
| 722 | C2×D4 | — | 6 | 1 | no | — |
| 723 | C2×D4 | — | 6 | 1 | no | — |
| 724 | C2×D4 | — | 6 | 2 | no | — |
| 725 | C2×D4 | — | 6 | 2 | no | — |
| 726 | C2×D4 | — | 6 | 1 | no | — |
| 727 | C2×D4 | — | 6 | 1 | no | — |
| 728 | C2×D4 | — | 6 | 1 | no | — |
| 729 | C2×D4 | — | 6 | 2 | no | — |
| 730 | C2×D4 | — | 6 | 2 | no | — |
| 731 | C2×D4 | — | 6 | 1 | no | — |
| 732 | C2×D4 | — | 6 | 2 | no | — |
| 733 | C2×D4 | — | 6 | 2 | no | — |
| 734 | C2×D4 | — | 6 | 2 | no | — |
| 735 | C2×D4 | — | 6 | 2 | no | — |
| 736 | C2×D4 | — | 6 | 4 | no | — |
| 737 | C2×D4 | — | 6 | 4 | no | — |
| 738 | C2×D4 | — | 6 | 8 | no | — |
| 739 | C2×D4 | — | 6 | 8 | no | — |
| 740 | C2×D4 | — | 6 | 8 | no | — |
| 741 | C2×D4 | — | 6 | 4 | no | — |
| 742 | C2×D4 | — | 12 | 1 | no | — |
| 743 | C2×D4 | — | 12 | 1 | no | — |
| 744 | C2×D4 | — | 12 | 2 | no | — |
| 745 | C2×D4 | — | 12 | 1 | no | — |
| 746 | C2×D4 | — | 12 | 1 | no | — |
| 747 | C2×D4 | — | 12 | 1 | no | — |
| 748 | C2×D4 | — | 12 | 1 | no | — |
| 749 | C2×D4 | — | 12 | 1 | no | — |
| 750 | C2×D4 | — | 12 | 1 | no | — |
| 751 | C2×D4 | — | 12 | 2 | no | — |
| 752 | C2×D4 | — | 12 | 2 | no | — |
| 753 | C2×D4 | — | 12 | 4 | no | — |
| 754 | C2×D4 | — | 12 | 4 | no | — |
| 755 | C2×D4 | — | 12 | 1 | no | — |
| 756 | C2×D4 | — | 12 | 2 | no | — |
| 757 | C2×D4 | — | 12 | 1 | no | — |
| 758 | C2×D4 | — | 12 | 2 | no | — |
| 759 | C2×D4 | — | 12 | 1 | no | — |
| 760 | C2×D4 | — | 12 | 2 | no | — |
| 761 | C2×D4 | — | 12 | 2 | no | — |
| 762 | C2×D4 | — | 12 | 1 | no | — |
| 763 | C2×D4 | — | 12 | 4 | no | — |
| 764 | C2×D4 | — | 12 | 8 | no | — |
| 765 | C2×D4 | — | 12 | 4 | no | — |
| 766 | C2×D4 | — | 12 | 1 | no | — |
| 767 | C2×D4 | — | 24 | 2 | no | — |
| 768 | C2×D4 | — | 24 | 2 | no | — |
| 769 | C2×D4 | — | 24 | 1 | no | — |
| 770 | C2×D4 | — | 24 | 1 | no | — |
| 771 | C2×D4 | — | 24 | 2 | no | — |
| 772 | C2×D4 | — | 24 | 4 | no | — |
| 773 | C2×D4 | — | 24 | 2 | no | — |
| 774 | C2×D4 | — | 24 | 4 | no | — |
| 775 | C2×D4 | — | 24 | 4 | no | — |
| 776 | C2×D4 | — | 24 | 2 | no | — |
| 777 | C2×D4 | — | 24 | 2 | no | — |
| 778 | C2×D4 | — | 48 | 4 | no | — |
| 779 | C2×D4 | — | 48 | 4 | no | — |
| 780 | C22×C4 | — | 2 | 2 | no | — |
| 781 | C22×C4 | — | 3 | 1 | no | — |
| 782 | C22×C4 | — | 3 | 1 | no | — |
| 783 | C22×C4 | — | 3 | 2 | no | — |
| 784 | C22×C4 | — | 3 | 1 | no | — |
| 785 | C22×C4 | — | 3 | 1 | no | — |
| 786 | C22×C4 | — | 3 | 2 | no | — |
| 787 | C22×C4 | — | 3 | 2 | no | — |
| 788 | C22×C4 | — | 3 | 2 | no | — |
| 789 | C22×C4 | — | 3 | 2 | no | — |
| 790 | C22×C4 | — | 4 | 1 | no | — |
| 791 | C22×C4 | — | 6 | 4 | no | — |
| 792 | C22×C4 | — | 6 | 1 | no | — |
| 793 | C22×C4 | — | 6 | 2 | no | — |
| 794 | C22×C4 | — | 6 | 1 | no | — |
| 795 | C22×C4 | — | 6 | 2 | no | — |
| 796 | C22×C4 | — | 6 | 4 | no | — |
| 797 | C22×C4 | — | 6 | 1 | no | — |
| 798 | C22×C4 | — | 6 | 1 | no | — |
| 799 | C22×C4 | — | 6 | 1 | no | — |
| 800 | C22×C4 | — | 6 | 1 | no | — |
| 801 | C22×C4 | — | 6 | 1 | no | — |
| 802 | C22×C4 | — | 6 | 2 | no | — |
| 803 | C22×C4 | — | 6 | 2 | no | — |
| 804 | C22×C4 | — | 6 | 2 | no | — |
| 805 | C22×C4 | — | 6 | 2 | no | — |
| 806 | C22×C4 | — | 6 | 1 | no | — |
| 807 | C22×C4 | — | 6 | 2 | no | — |
| 808 | C22×C4 | — | 6 | 1 | no | — |
| 809 | C22×C4 | — | 6 | 2 | no | — |
| 810 | C22×C4 | — | 6 | 1 | no | — |
| 811 | C22×C4 | — | 6 | 4 | no | — |
| 812 | C22×C4 | — | 6 | 8 | no | — |
| 813 | C22×C4 | — | 6 | 8 | no | — |
| 814 | C22×C4 | — | 12 | 2 | no | — |
| 815 | C22×C4 | — | 12 | 1 | no | — |
| 816 | C22×C4 | — | 12 | 2 | no | — |
| 817 | C22×C4 | — | 12 | 1 | no | — |
| 818 | C22×C4 | — | 12 | 2 | no | — |
| 819 | C22×C4 | — | 24 | 2 | no | — |
| 820 | C22×C4 | — | 24 | 1 | no | — |
| 821 | C22×C4 | — | 24 | 1 | no | — |
| 822 | C22×C4 | — | 24 | 1 | no | — |
| 823 | C22×C4 | — | 24 | 4 | no | — |
| 824 | C22×C4 | — | 24 | 2 | no | — |
| 825 | C22×C4 | C22×S4 | 1 | 2 | yes | — |
| 826 | C22×C4 | C22×S4 | 1 | 2 | yes | — |
| 827 | Q16 | — | 12 | 4 | no | — |
| 828 | Q16 | — | 12 | 4 | no | — |
| 829 | Q16 | — | 12 | 8 | no | — |
| 830 | SD16 | — | 12 | 4 | no | — |
| 831 | SD16 | — | 12 | 4 | no | — |
| 832 | SD16 | — | 12 | 8 | no | — |
| 833 | M16 | — | 6 | 4 | no | — |
| 834 | M16 | — | 12 | 2 | no | — |
| 835 | M16 | — | 12 | 4 | no | — |
| 836 | C2×C8 | — | 12 | 4 | no | — |
| 837 | C2×C8 | — | 12 | 2 | no | — |
| 838 | C4⋊C4 | — | 6 | 4 | no | — |
| 839 | C4⋊C4 | — | 6 | 4 | no | — |
| 840 | C4⋊C4 | — | 6 | 4 | no | — |
| 841 | C4⋊C4 | — | 6 | 2 | no | — |
| 842 | C4⋊C4 | — | 6 | 2 | no | — |
| 843 | C4⋊C4 | — | 6 | 4 | no | — |
| 844 | C4⋊C4 | — | 6 | 8 | no | — |
| 845 | C4⋊C4 | — | 6 | 8 | no | — |
| 846 | C4⋊C4 | — | 6 | 8 | no | — |
| 847 | C4⋊C4 | — | 6 | 8 | no | — |
| 848 | C4⋊C4 | — | 6 | 8 | no | — |
| 849 | C4⋊C4 | — | 12 | 4 | no | — |
| 850 | C22⋊C4 | — | 3 | 4 | no | — |
| 851 | C22⋊C4 | — | 3 | 2 | no | — |
| 852 | C22⋊C4 | — | 3 | 2 | no | — |
| 853 | C22⋊C4 | — | 6 | 4 | no | — |
| 854 | C22⋊C4 | — | 6 | 4 | no | — |
| 855 | C22⋊C4 | — | 6 | 4 | no | — |
| 856 | C22⋊C4 | — | 6 | 8 | no | — |
| 857 | C22⋊C4 | — | 6 | 2 | no | — |
| 858 | C22⋊C4 | — | 6 | 2 | no | — |
| 859 | C22⋊C4 | — | 6 | 2 | no | — |
| 860 | C22⋊C4 | — | 6 | 1 | no | — |
| 861 | C22⋊C4 | — | 6 | 1 | no | — |
| 862 | C22⋊C4 | — | 6 | 2 | no | — |
| 863 | C22⋊C4 | — | 6 | 2 | no | — |
| 864 | C22⋊C4 | — | 6 | 4 | no | — |
| 865 | C22⋊C4 | — | 6 | 4 | no | — |
| 866 | C22⋊C4 | — | 6 | 4 | no | — |
| 867 | C22⋊C4 | — | 6 | 4 | no | — |
| 868 | C22⋊C4 | — | 6 | 4 | no | — |
| 869 | C22⋊C4 | — | 6 | 8 | no | — |
| 870 | C22⋊C4 | — | 6 | 8 | no | — |
| 871 | C22⋊C4 | — | 6 | 8 | no | — |
| 872 | C22⋊C4 | — | 6 | 8 | no | — |
| 873 | C22⋊C4 | — | 6 | 8 | no | — |
| 874 | C22⋊C4 | — | 6 | 8 | no | — |
| 875 | C22⋊C4 | — | 6 | 4 | no | — |
| 876 | C22⋊C4 | — | 6 | 4 | no | — |
| 877 | C22⋊C4 | — | 12 | 8 | no | — |
| 878 | C22⋊C4 | — | 12 | 4 | no | — |
| 879 | C22⋊C4 | — | 12 | 4 | no | — |
| 880 | C22⋊C4 | — | 12 | 2 | no | — |
| 881 | C42 | — | 3 | 4 | no | — |
| 882 | C42 | — | 6 | 2 | no | — |
| 883 | C42 | — | 6 | 4 | no | — |
| 884 | C42 | — | 6 | 4 | no | — |
| 885 | C42 | — | 6 | 8 | no | — |
| 886 | C42 | — | 6 | 8 | no | — |
| 887 | C42 | — | 12 | 4 | no | — |
| 888 | C22×C3 | — | 16 | 2 | no | — |
| 889 | C22×C3 | — | 16 | 1 | no | — |
| 890 | C22×C3 | — | 32 | 2 | no | — |
| 891 | C2×D3 | — | 16 | 4 | no | — |
| 892 | C2×D3 | — | 32 | 4 | no | — |
| 893 | A4 | — | 4 | 1 | no | — |
| 894 | A4 | — | 8 | 1 | no | — |
| 895 | C3×C4 | — | 16 | 2 | no | — |
| 896 | C3×C4 | — | 16 | 2 | no | — |
| 897 | Dic3 | — | 16 | 4 | no | — |
| 898 | C23 | — | 2 | 1 | no | — |
| 899 | C23 | — | 3 | 1 | no | — |
| 900 | C23 | — | 3 | 1 | no | — |
| 901 | C23 | — | 3 | 1 | no | — |
| 902 | C23 | — | 3 | 1 | no | — |
| 903 | C23 | — | 3 | 2 | no | — |
| 904 | C23 | — | 4 | 1 | no | — |
| 905 | C23 | — | 4 | 2 | no | — |
| 906 | C23 | — | 6 | 2 | no | — |
| 907 | C23 | — | 6 | 1 | no | — |
| 908 | C23 | — | 6 | 1 | no | — |
| 909 | C23 | — | 6 | 4 | no | — |
| 910 | C23 | — | 6 | 1 | no | — |
| 911 | C23 | — | 6 | 1 | no | — |
| 912 | C23 | — | 6 | 2 | no | — |
| 913 | C23 | — | 6 | 1 | no | — |
| 914 | C23 | — | 8 | 2 | no | — |
| 915 | C23 | — | 8 | 2 | no | — |
| 916 | C23 | — | 12 | 1 | no | — |
| 917 | C23 | — | 12 | 2 | no | — |
| 918 | C23 | — | 12 | 1 | no | — |
| 919 | C23 | — | 12 | 2 | no | — |
| 920 | C23 | — | 12 | 2 | no | — |
| 921 | C23 | — | 12 | 2 | no | — |
| 922 | C23 | — | 12 | 2 | no | — |
| 923 | C23 | — | 12 | 4 | no | — |
| 924 | C23 | — | 12 | 4 | no | — |
| 925 | C23 | — | 12 | 4 | no | — |
| 926 | C23 | — | 12 | 2 | no | — |
| 927 | C23 | — | 24 | 2 | no | — |
| 928 | C23 | — | 24 | 4 | no | — |
| 929 | C23 | — | 24 | 2 | no | — |
| 930 | C23 | — | 24 | 4 | no | — |
| 931 | C23 | — | 24 | 2 | no | — |
| 932 | C23 | — | 24 | 4 | no | — |
| 933 | C23 | — | 24 | 4 | no | — |
| 934 | C23 | — | 48 | 4 | no | — |
| 935 | C23 | C23×S4 | 1 | 1 | yes | characteristic |
| 936 | Q8 | — | 2 | 1 | no | — |
| 937 | Q8 | — | 6 | 1 | no | — |
| 938 | Q8 | — | 6 | 2 | no | — |
| 939 | Q8 | — | 12 | 2 | no | — |
| 940 | Q8 | — | 12 | 2 | no | — |
| 941 | Q8 | — | 12 | 4 | no | — |
| 942 | Q8 | — | 12 | 1 | no | — |
| 943 | Q8 | — | 12 | 4 | no | — |
| 944 | Q8 | — | 12 | 4 | no | — |
| 945 | Q8 | — | 24 | 2 | no | — |
| 946 | Q8 | — | 24 | 8 | no | — |
| 947 | D4 | — | 6 | 1 | no | — |
| 948 | D4 | — | 6 | 1 | no | — |
| 949 | D4 | — | 6 | 2 | no | — |
| 950 | D4 | — | 12 | 2 | no | — |
| 951 | D4 | — | 12 | 2 | no | — |
| 952 | D4 | — | 12 | 4 | no | — |
| 953 | D4 | — | 12 | 1 | no | — |
| 954 | D4 | — | 12 | 1 | no | — |
| 955 | D4 | — | 12 | 2 | no | — |
| 956 | D4 | — | 12 | 2 | no | — |
| 957 | D4 | — | 12 | 1 | no | — |
| 958 | D4 | — | 12 | 1 | no | — |
| 959 | D4 | — | 12 | 1 | no | — |
| 960 | D4 | — | 12 | 2 | no | — |
| 961 | D4 | — | 12 | 2 | no | — |
| 962 | D4 | — | 12 | 1 | no | — |
| 963 | D4 | — | 12 | 4 | no | — |
| 964 | D4 | — | 24 | 4 | no | — |
| 965 | D4 | — | 24 | 8 | no | — |
| 966 | D4 | — | 24 | 4 | no | — |
| 967 | D4 | — | 24 | 4 | no | — |
| 968 | D4 | — | 24 | 8 | no | — |
| 969 | D4 | — | 24 | 4 | no | — |
| 970 | D4 | — | 24 | 8 | no | — |
| 971 | D4 | — | 24 | 2 | no | — |
| 972 | D4 | — | 24 | 2 | no | — |
| 973 | D4 | — | 48 | 4 | no | — |
| 974 | D4 | — | 48 | 4 | no | — |
| 975 | D4 | — | 48 | 8 | no | — |
| 976 | C2×C4 | — | 3 | 1 | no | — |
| 977 | C2×C4 | — | 3 | 2 | no | — |
| 978 | C2×C4 | — | 3 | 2 | no | — |
| 979 | C2×C4 | — | 3 | 2 | no | — |
| 980 | C2×C4 | — | 3 | 1 | no | — |
| 981 | C2×C4 | — | 3 | 1 | no | — |
| 982 | C2×C4 | — | 3 | 2 | no | — |
| 983 | C2×C4 | — | 4 | 1 | no | — |
| 984 | C2×C4 | — | 4 | 4 | no | — |
| 985 | C2×C4 | — | 6 | 1 | no | — |
| 986 | C2×C4 | — | 6 | 2 | no | — |
| 987 | C2×C4 | — | 6 | 2 | no | — |
| 988 | C2×C4 | — | 6 | 2 | no | — |
| 989 | C2×C4 | — | 6 | 2 | no | — |
| 990 | C2×C4 | — | 6 | 2 | no | — |
| 991 | C2×C4 | — | 6 | 1 | no | — |
| 992 | C2×C4 | — | 6 | 1 | no | — |
| 993 | C2×C4 | — | 6 | 1 | no | — |
| 994 | C2×C4 | — | 6 | 1 | no | — |
| 995 | C2×C4 | — | 6 | 2 | no | — |
| 996 | C2×C4 | — | 6 | 2 | no | — |
| 997 | C2×C4 | — | 6 | 2 | no | — |
| 998 | C2×C4 | — | 6 | 2 | no | — |
| 999 | C2×C4 | — | 6 | 2 | no | — |
| 1000 | C2×C4 | — | 6 | 1 | no | — |
| 1001 | C2×C4 | — | 6 | 1 | no | — |
| 1002 | C2×C4 | — | 6 | 4 | no | — |
| 1003 | C2×C4 | — | 6 | 2 | no | — |
| 1004 | C2×C4 | — | 6 | 4 | no | — |
| 1005 | C2×C4 | — | 6 | 2 | no | — |
| 1006 | C2×C4 | — | 6 | 4 | no | — |
| 1007 | C2×C4 | — | 12 | 4 | no | — |
| 1008 | C2×C4 | — | 12 | 1 | no | — |
| 1009 | C2×C4 | — | 12 | 1 | no | — |
| 1010 | C2×C4 | — | 12 | 2 | no | — |
| 1011 | C2×C4 | — | 12 | 2 | no | — |
| 1012 | C2×C4 | — | 12 | 1 | no | — |
| 1013 | C2×C4 | — | 12 | 2 | no | — |
| 1014 | C2×C4 | — | 12 | 2 | no | — |
| 1015 | C2×C4 | — | 12 | 4 | no | — |
| 1016 | C2×C4 | — | 12 | 4 | no | — |
| 1017 | C2×C4 | — | 12 | 2 | no | — |
| 1018 | C2×C4 | — | 12 | 2 | no | — |
| 1019 | C2×C4 | — | 12 | 4 | no | — |
| 1020 | C2×C4 | — | 24 | 8 | no | — |
| 1021 | C2×C4 | — | 24 | 4 | no | — |
| 1022 | C2×C4 | — | 24 | 8 | no | — |
| 1023 | C2×C4 | — | 24 | 4 | no | — |
| 1024 | C2×C4 | #1020⋊C2 | 1 | 1 | yes | characteristic |
| 1025 | C8 | — | 12 | 4 | no | — |
| 1026 | C2×C3 | — | 16 | 2 | no | — |
| 1027 | C2×C3 | — | 16 | 1 | no | — |
| 1028 | C2×C3 | — | 32 | 2 | no | — |
| 1029 | D3 | — | 32 | 4 | no | — |
| 1030 | C22 | — | 3 | 1 | no | — |
| 1031 | C22 | — | 3 | 1 | no | — |
| 1032 | C22 | — | 4 | 1 | no | — |
| 1033 | C22 | — | 4 | 2 | no | — |
| 1034 | C22 | — | 6 | 2 | no | — |
| 1035 | C22 | — | 6 | 1 | no | — |
| 1036 | C22 | — | 6 | 2 | no | — |
| 1037 | C22 | — | 6 | 1 | no | — |
| 1038 | C22 | — | 8 | 2 | no | — |
| 1039 | C22 | — | 8 | 1 | no | — |
| 1040 | C22 | — | 12 | 1 | no | — |
| 1041 | C22 | — | 12 | 2 | no | — |
| 1042 | C22 | — | 12 | 2 | no | — |
| 1043 | C22 | — | 12 | 2 | no | — |
| 1044 | C22 | — | 12 | 1 | no | — |
| 1045 | C22 | — | 12 | 1 | no | — |
| 1046 | C22 | — | 12 | 4 | no | — |
| 1047 | C22 | — | 12 | 4 | no | — |
| 1048 | C22 | — | 12 | 2 | no | — |
| 1049 | C22 | — | 12 | 2 | no | — |
| 1050 | C22 | — | 12 | 4 | no | — |
| 1051 | C22 | — | 24 | 2 | no | — |
| 1052 | C22 | — | 24 | 1 | no | — |
| 1053 | C22 | — | 24 | 1 | no | — |
| 1054 | C22 | — | 24 | 4 | no | — |
| 1055 | C22 | — | 24 | 1 | no | — |
| 1056 | C22 | — | 24 | 2 | no | — |
| 1057 | C22 | — | 24 | 4 | no | — |
| 1058 | C22 | — | 24 | 4 | no | — |
| 1059 | C22 | — | 24 | 4 | no | — |
| 1060 | C22 | — | 48 | 1 | no | — |
| 1061 | C22 | — | 48 | 4 | no | — |
| 1062 | C22 | C2×#1020⋊C2 | 1 | 1 | yes | characteristic |
| 1063 | C4 | — | 3 | 2 | no | — |
| 1064 | C4 | — | 4 | 2 | no | — |
| 1065 | C4 | — | 6 | 1 | no | — |
| 1066 | C4 | — | 6 | 2 | no | — |
| 1067 | C4 | — | 6 | 1 | no | — |
| 1068 | C4 | — | 12 | 2 | no | — |
| 1069 | C4 | — | 12 | 4 | no | — |
| 1070 | C4 | — | 12 | 4 | no | — |
| 1071 | C4 | — | 12 | 2 | no | — |
| 1072 | C4 | — | 12 | 4 | no | — |
| 1073 | C4 | — | 24 | 4 | no | — |
| 1074 | C4 | C2×#1020⋊C2 | 1 | 2 | yes | — |
| 1075 | C3 | — | 16 | 1 | no | Sylow |
| 1076 | C2 | — | 6 | 1 | no | — |
| 1077 | C2 | — | 6 | 1 | no | — |
| 1078 | C2 | — | 8 | 2 | no | — |
| 1079 | C2 | — | 12 | 1 | no | — |
| 1080 | C2 | — | 12 | 2 | no | — |
| 1081 | C2 | — | 12 | 1 | no | — |
| 1082 | C2 | — | 24 | 4 | no | — |
| 1083 | C2 | #11714179 | 1 | 2 | yes | direct product factor |
| 1084 | C2 | C22×#1020⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#1020⋊C2 |
| commutator, cosocle, hypocenter | #997 | C24 |
| Frattini | C23 | C23×S4 |
| Fitting | C2×#3025 | D3 |
| hypercenter | C2×C4 | #1020⋊C2 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87521 | C2 | semidirect |
| 2. C2×#87518 | C2 | semidirect |
| 3. #11714179 | C2 | direct (N × H) |
| 4. C2×#73027 | C2 | semidirect |
| 5. C2×#73030 | C2 | semidirect |
| 6. C2×#3025⋊C3 | C2 | semidirect |
| 9. #87521 | C22 | semidirect |
| 10. #87518 | C22 | semidirect |
| 14. #3025⋊C3 | C22 | semidirect |
| 17. #73030 | C22 | semidirect |
| 18. #73027 | C22 | semidirect |
| 21. C2×#3025 | D3 | semidirect |
| 72. #3025 | C2×D3 | semidirect |
| 138. C24×C4 | S4 | semidirect |
| 424. C23×C4 | C2×S4 | semidirect |
| 1083. C2 | #11714179 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87521 | 2 |
| C2×#87518 | 2 |
| #11714179 | 2 |
| C2×#73027 | 2 |
| C2×#73030 | 2 |
| C2×#3025⋊C3 | 2 |
| C2×#33555 | 3 |
| C2×#5912 | 4 |